Reading: The Challenges of Relative Valuation

To the extent that control, liquidity, and synergy are valuable, different valuation situations will produce systematically different valuation levels for the same firm depending on the type of transaction we consider. For example, a full-firm acquisition will generally fetch a higher price than a minority-stake acquisition. The reason is that the former transaction gives him full control over the firm's activities whereas the latter only makes him a "junior partner," possibly without too much saying in strategic decisions.

 

When analyzing different transactions, we should therefore always investigate their implications for control, liquidity, and synergy. We are looking for answers to the following three questions:

• Control: Does the transaction involve a controlling stake or are minority shareholders dealing? 

• Liquidity: Can the asset in question easily be bought and sold (is the market for the asset liquid)?

• Synergy: Do we expect synergy effects from the transaction?

  

The following table summarizes the typical answers to the above questions for the various valuation approaches and situations that we have considered before. The benchmark (top row) is the Discounted cash flow (DCF) approach, which is the main topic of the course bundle Firm Valuation. 

  

  

For a better understanding, let us discuss some of the entries in the table:

• With the DCF approach, we generally assume control (we look at the full cash flow and allow for management changes in the key value drivers over time). By using very liquid assets as benchmark returns, we also assume that the market for the firm's capital is liquid. Finally, the standard DCF does generally not include synergy, though that could be easily implemented.
• With trading multiples, we generally do not assume control, as stock prices reflect the prices that shareholders pay to exchange small fractions of the firm's equity. We assume liquidity, as there is an organized market to bring buyers and sellers together. Finally, we typically assume no synergy.

  

Consequently, DCF and trading multiples differ with respect to their (implicit) assumption about control. DCF values the whole capital whereas trading multiples reflect minority deals. If control is valuable, we would therefore expect that the DCF approach produces systematically higher valuations than trading multiples---the difference between the two could be the so-called minority discount.

   

Similarly, we should not be surprised to find systematic differences between strategic transaction multiples and financial transaction multiples, as the former often entail a synergy premium whereas the latter don't (an acquisition by a strategic buyer often fetches a higher price than a buyout by a private equity fund).

  

How Valuable are Control, Liquidity, and Synergy

Extensive academic and applied research shows that control, liquidity, and synergy are valuable. A discussion of this literature goes far beyond the scope of this introductory module. The problem is that it is not straightforward to measure the value implications of these three dimensions, as they depend significantly on the specific situation of the firm in question. 

  

• For example, to what extent minority shareholders discount their valuation depends on the firm's business model (how important is it to be in control?), the ownership structure (who are the majority shareholders? and how will they behave in the future), the legal environment (how well are minority shareholders protected?) etc. 
• Similarly, the value of liquidity depends on the firm's business model (e.g., volatility of cash flows), asset structure (can the assets easily be sold?), preferences of the shareholders (long-term vs. short-term focus), etc. 
• Finally, the value of synergy depends on what the acquirer can do with the target firm, e.g., whether the acquisition of the target firm will allow the acquirer to grow its market share, reduce costs, etc. It also depends on how expensive and complicated it is to integrate the target firm and change its activities.

  

To get a very rough idea of the value relevance of control, liquidity, and synergy, here are some typical discounts/premia that are often encountered in practice:

• Minority discount: 20%
• Discount for lack of liquidity: 30%
• Synergy premium (net of costs): 15%

  

In words, it is not unusual to observe that: 

• minority stakes trade at a price that is 20% below the price of a majority stake;
• illiquid assets are valued 30% lower than liquid assets
• acquirers who expect to generate synergies pay 15% more than acquirers without such synergies.

  
Clearly, these considerations have far-reaching valuation implications. This is exactly what the following examples illustrate.

  

Example 1:

Suppose we want to value the equity of a privately held firm with a net income of 5 million. The transaction we have in mind is the sale of a minority stake (e.g., 20%) to a financial buyer. The only valuation multiples that are available are trading multiples. According to these trading multiples, the typical P/E ratio of listed comparable firms is 20. 

Based on this information, and using the discounts/premia from above, what is the potential valuation of the deal in question? 

  

If our firm was listed on a stock exchange, the answer would be 100 million, i.e., the firm's net income (5 million) times the typical P/E ratio of listed comparable firms (20). 

This, however, is not the transaction that we are considering. We are looking at a financial deal that involves a minority stake in an unlisted company. The table above shows that the two valuation situations (trading multiples vs. transaction multiples for minority financial deals) differ with respect to the liquidity of the asset. Assuming an illiquidity discount of 30%, the "fair" valuation drops to 70 million, namely:

   

   

Because the asset in question is illiquid, the buyer will not be willing to pay the full price. 

  

Example 2:

Let us consider the same firm in a different valuation setting. Now suppose the firm wanted to sell a majority stake to a financial buyer. The difference to the preceding example is that the transaction now entails control. If minority transactions are conducted at a discount of 20% according to the list above, we would expect that the previous valuation (70 million for a minority stake) is 20% below the valuation a majority buyer is willing to pay:

  

  

Since we are interested in the value of the majority deal, the relevant we solve the above equation for that argument:

  

Value majority illiquid = Value minority illiquid / (1 - minority discount) = 70/0.8 = 87.5 million.

   

Consequently, a fair valuation could be 87.5 million. The difference of 17.5 million to the preceding valuation reflects the fact that buyers are generally more willing to pay for transactions that give them full control over the acquired assets.

   

Example 3:

Now let's assume that the firm could also sell the majority to a strategic buyer. How would this affect our analysis, assuming a synergy premium of 15%?

If strategic buyers are willing to pay a premium of 15% compared to the same transaction with a financial buyer, the resulting price should also be 15% higher, namely 100.6 million:

  

Discussion

The previous examples have illustrated the value relevance of control, liquidity, and synergy. Depending on the specific type of transaction that we have in mind, the resulting valuation can be substantially different. In the above examples, the "fair" values ranged from more than 100 million in the case of a strategic full-firm acquisition to 70 million in the case of a minority financial deal. The implications of this are at least twofold:

  

• When valuing firms, we have to be consistent with respect to the three dimensions control, liquidity, and synergy.
• More importantly, from a strategic point of view, we have to understand that different strategic options will have different values. Consequently, we shoud make sure that the management checks all the options and works on those options that promise the highest value!